Asymptotics for at the money local vol basket options

We consider a basket or spread option on based on a multi-dimensional local volatility model. Bayer and Laurence [Comm. Pure. Appl. Math., to appear] derived highly accurate analytic formulas for prices and implied volatilities of such options when the options are not at the money. We now extend these results to the ATM case. Moreover, we also derive similar formulas for the local volatility of the basket